starting my first carputer project, have some questions

hey guys, im a fairly new member, and have been asked to install a carputer into my friends corolla. This, of course, is a budgeted plan, and I have a few questions to ask before i wire everything up. We will be using a 400w power inverter to power the psu, and i will tap into a 12v line to run the lilliput monitor. We only want the computer to be able to be on when the key is in the ACC position, so i will implement a relay using these guidelines: sry dont have pics (im at school)

after pin 87a, i would like to run a time delay diode (terminology?) that for sure cuts power after a few min in order to prevent batt drain- don't have a deep cycle battery.

i know that the 87 pin hot wire will work as power, but does anyone think that the switch between 87 and 87a will be too slow and the puter just crash. this is the only way that i can think of with my limited knowledge to still supply power to the puter after the key is off. any suggestions will help.

also, to power the lilliput, i want to run it from a 12v+ all time hot src, but my friend wants to run it from the other ac plug in after the inverter. i said no, because this will put more strain on the inverter, and you wouldn't be able to use the extra socket for any other things, in case ya know !
the question is, what is the best way to power the lilliput, and what rating of fuse should i use- i am imagining that it will only be a couple mA. again, suggestions would be appreciated.

sorry this is getting so long but- should i be concerned with heat issues from the inverter? it willbe mounted on the psu, with the hardrive suspended above it, with about .75" of clearance between hd and inverter for airflow. this assembly will all be mounted in the dash, behind and beneath the lilliput. we hope to mount the mobo in the glove compartment, but might have issues with clearance, ill cross that bridge when i get there!

i guess the main questions are:
1) will switch time between relay pins 87 and 87a be quick enuff to not cause the puter to crash, and will my idea work as a delayed power shutoff?
2) how should i power the lilliput, and what kind of fuse to use if i go from a 12v src?
3)will heat be an issue, and u can throw in, how have you mounted ur mobo?

sry for the length, but i cant ever seem to get my friend to research anything about it,and i am really pressed for time, and it doesnt help that his thriftyness is killing me on the proper way to wire things (imo) "he thinks im fuse crazy" im just worried about blowing a $300 screen, and a $180 mobo
once again guys, thanks for ur help

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